Robust control charts for the mean of a locally linear time series

We study residual control charts for the detection of sudden changes in time series with an underlying time-varying trend. Our control charts compare the most recent observations to their direct predecessors by applying two-sample tests in a moving time window to one-step-ahead prediction errors obtained from a local linear regression. Global model assumptions, a fixed target value, or large sets of historical in-control data are unnecessary therefore. Disturbing in-control structures, like short outlier patches or minor fluctuations, are resisted by using robust methods. Our simulation results indicate that a control chart based on the two-sample Hodges-Lehmann estimator in combination with repeated-median regression possesses an approximately distribution-free in-control average run length, good robustness against outliers, and a desirable detection quality.